Statistical estimation in passenger‐to‐train assignment models based on automated data

Abstract

With the rapid development of metro systems, it has become increasingly important to study phenomena such as passenger flow distribution and passenger boarding behavior. It is difficult for existing methods to accurately describe actual situations and to extend to the whole metro system due to the limitations from parameter uncertainties in their mathematical models. In this article, we propose a passenger‐to‐train assignment model to evaluate the probabilities of individual passengers boarding each feasible train for both no‐transfer and one‐transfer situations. This model can be used to understand passenger flows and crowdedness. The input parameters of the model include the probabilities that the passengers take each train and the probability distribution of egress time, which is the time to walk to the tap‐out fare gate after alighting from the train. We present the likelihood method to estimate these parameters based on data from the automatic fare collection and automatic vehicle location systems. This method can construct several nonparametric density estimates without assuming the parametric form of the distribution of egress time. The EM algorithm is used to compute the maximum likelihood estimates. Simulation results indicate that the proposed estimates perform well. By applying our method to real data in Beijing metro system, we can identify different passenger flow patterns between peak and off‐peak hours.

Bayesian Analysis for Metro Passenger Flows Using Automated Data

“…is article presents a Bayesian analysis of the statistical models of AFC data in both no-transfer and one-transfer situations. Our work extends Xiong et al [16] in the following two directions. First, Xiong et al [16] provided only point estimation for the parameters that lacks uncertainty quantification.…”

“…Our work extends Xiong et al [16] in the following two directions. First, Xiong et al [16] provided only point estimation for the parameters that lacks uncertainty quantification. Instead, we propose a Bayesian inferential method to quantify the uncertainty of parameter estimation.…”

“…Interval estimation for the parameters and related passengers' indices can be derived. Second, we show that Xiong et al [16]'s estimation method cannot be straightforwardly extended to one-transfer situations due to an identifiability problem. With some prior information, our Bayesian method avoids this problem and yields reasonable estimators.…”

“…We make the Bayesian inference for the metro passenger flow including estimating the probabilities of taking trains and the probability density functions of egress time, where egress time is the time it takes to walk to the tap-out fare gate after alighting from the train. Since millions of people take metro trains everyday in big cities like Beijing, it is not difficult to collect sufficient data from passengers whose tap-in times are almost the same in large stations [16]. Suppose we get the AFC data of n passengers whose tap-in times are t 0 .…”

“…With only AFC data, few studies presented accurate probability distribution models. Recently, Xiong et al [16] have proposed a new passenger-to-train assignment model. By deriving the probability distributions of AFC data, they provided maximum-likelihood estimates of unknown parameters in this model in no-transfer situations.…”